We investigate stability of convective flows in a layer with stress-free horizontal boundaries near the onset of convection. In a rotating layer the flows near the onset (rolls, standing and travelling waves) are always unstable to perturbations, which are linear combinations of large-scale modes and short-scale modes, whose wave numbers are close to those of the perturbed flows. In a non-rotating flows the stability of rolls depends on the Prandtl number, for small Prandtl numbers, no stable rolls exist near the onset.